Stacy is painting her bedroom. She is able to paint 3/4 of the bedroom in 3 hours. At this rate, how long will it take her to paint the entire room? Fractions
To solve this problem, we can set up a proportion.
If Stacy can paint 3/4 of the bedroom in 3 hours, we can say:
3 hours = 3/4 of the bedroom
To find out how long it will take her to paint the entire room, we can set up the proportion:
3 hours / (3/4 of the bedroom) = x hours / (1 bedroom)
To simplify this proportion, we can multiply both sides by the reciprocal of (3/4 of the bedroom):
3 hours * (4/3 of the bedroom) = x hours
Canceling out common factors:
4 hours = x hours
Therefore, it will take Stacy 4 hours to paint the entire room.
Miguel is returning from a trip. In 4 hours, he has driven 2/ of the total distance. He wants to know how long the total drive will take. At this rate, what is the total time it will take him to reach his destination? Fractions
To solve this problem, we can set up a proportion.
If Miguel has driven 2/3 of the total distance in 4 hours, we can say:
4 hours = 2/3 of the total distance
To find out how long the total drive will take, we can set up the proportion:
4 hours / (2/3 of the total distance) = x hours / (1 total distance)
To simplify this proportion, we can multiply both sides by the reciprocal of (2/3 of the total distance):
4 hours * (3/2 of the total distance) = x hours
Canceling out common factors:
6 hours = x hours
Therefore, it will take Miguel 6 hours to reach his destination.
Iris is asked to sweep the gymnasium floor after a basketball game. This requires her to push a sweeper from one end of the gym to the other and repeating the pattern until she has covered the entire floor. She completes 2/3 of the floor in 1/3 of an hour. At this rate, how long will it take her to complete the entire floor? Fractions
To solve this problem, we can set up a proportion.
If Iris completes 2/3 of the floor in 1/3 of an hour, we can say:
1/3 hour = 2/3 of the floor
To find out how long it will take her to complete the entire floor, we can set up the proportion:
1/3 hour / (2/3 of the floor) = x hours / (1 floor)
To simplify this proportion, we can multiply both sides by the reciprocal of (2/3 of the floor):
1/3 hour * (3/2 of the floor) = x hours
Canceling out common factors:
1/2 hour = x hours
Therefore, it will take Iris 1/2 hour to complete the entire floor.
To solve this problem, we need to find the amount of time it will take Stacy to paint the entire room based on the rate at which she is painting.
Given:
Stacy can paint 3/4 of the bedroom in 3 hours.
Step 1: Find the fraction of the room that Stacy can paint in a single hour.
To find the fraction of the room that Stacy can paint in one hour, divide 3/4 (the amount she can paint in 3 hours) by 3.
3/4 ÷ 3 = 1/4
So, Stacy can paint 1/4 of the bedroom in one hour.
Step 2: Determine the number of hours it will take Stacy to paint the entire room.
Since Stacy can paint 1/4 of the room in one hour, we can set up the following equation to find the number of hours it will take her to paint the entire room:
1/4 * x = 1
Where x represents the number of hours it will take Stacy to paint the entire room.
To solve for x, we multiply both sides of the equation by 4:
1/4 * x * 4 = 1 * 4
x = 4
Hence, it will take Stacy 4 hours to paint the entire room.
To find out how long it will take Stacy to paint the entire room, we need to determine the time it takes for one unit of work. In this case, one unit of work is equivalent to painting 3/4 of the bedroom.
Given that Stacy can complete 3/4 of the bedroom in 3 hours, we can set up a proportion to find the time needed to complete the entire room.
Let "x" represent the time needed to paint the entire room.
The proportion can be set up as follows:
(3/4) / 3 = 1 / x
We can cross-multiply to solve for x:
(3/4) * x = 3 * 1
Now, we can simplify the equation:
3x/4 = 3
To eliminate the fraction in the equation, we can multiply both sides by the reciprocal of 4/1, which is 1/4:
(1/4) * (3x/4) = (1/4) * 3
This gives us:
3x/16 = 3/4
To get rid of the denominator on the left side of the equation, we can multiply both sides by 16:
(3x/16) * 16 = (3/4) * 16
This simplifies to:
3x = 12
Finally, we can isolate "x" by dividing both sides by 3:
(3x)/3 = 12/3
This gives us:
x = 4
Therefore, it will take Stacy 4 hours to paint the entire room.